Grinsell (’folklore of prehistoric sites in Britain’) does not explain the folklore that goes with this site very much – but it sounds rather like your witch/giantess/devil + broken apron strings story: he says the stone was being carried by a (presumably rather large) old woman, and that it fell to the ground when one of her withies broke (withies are ropes made of long whippy willow twigs). (story recorded 1927).